What is 3x^2-2y^2-12x+12y+29=0 ?

The solution to 3x^2-2y^2-12x+12y+29=0 is Hyperbola with (h,k)=(2,3),a=sqrt(35/2),b=sqrt(35/3)

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3x^2-2y^2-12x+12y+29=0

3 x^{2} - 2 y^{2} - 12 x + 12 y + 29 = 0

(h, k) = (2, 3), a = \frac{35}{2}, b = \frac{35}{3}

Solution steps

3 x^{2} - 2 y^{2} - 12 x + 12 y + 29 = 0

Rewrite

3 x^{2} - 2 y^{2} - 12 x + 12 y + 29 = 0

in the form of a standard hyperbola equation

\frac{( y - 3 ) ^{2}}{( \frac{35}{2} ) ^{2}} - \frac{( x - 2 ) ^{2}}{( \frac{35}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 3), a = \frac{35}{2}, b = \frac{35}{3}

9 x^{2} - 4 y^{2} + 36 x + 8 y + 33 = 0

(x - 5)^{2} - (y - 4)^{2} = 1

144 x^{2} - 25 y^{2} + 864 x - 100 y - 2404 = 0

25 x^{2} - 16 y^{2} + 50 x + 128 y - 631 = 0

4 x^{2} - 4 y^{2} = 16

What is 3x^2-2y^2-12x+12y+29=0 ?
The solution to 3x^2-2y^2-12x+12y+29=0 is Hyperbola with (h,k)=(2,3),a=sqrt(35/2),b=sqrt(35/3)